{"paper":{"title":"Invariants recovering the reduction type of a hyperelliptic curve","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Elisa Lorenzo, Lilybelle Cowland Kellock","submitted_at":"2025-02-12T15:22:23Z","abstract_excerpt":"Tate's algorithm tells us that for an elliptic curve $E$ over a local field $K$ of residue characteristic $\\geq 5$, $E/K$ has potentially good reduction if and only if $\\text{ord}(j_E)\\geq 0$. It also tells us that when $E/K$ is semistable the dual graph of the special fibre of the minimal regular model of $E/K^{\\text{unr}}$ can be recovered from $\\text{ord}(j_E)$. We generalise these results to hyperelliptic curves of genus $g\\geq 2$ over local fields of odd residue characteristic $K$ by defining a list of absolute invariants that determine the potential stable model of a genus $g$ hyperellip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08487","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.08487/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}